Latest Elitmus Aptitude Question SOLUTION: HOW MANY 3 DIGITS NUMBERS ARE THERE WHOSE SUM IS 18?

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(#M40114511) ELITMUS Numerical Ability question APTITUDE Keep an EYE

HOW MANY 3 DIGITS NUMBERS ARE THERE WHOSE SUM IS 18?

Asked In Elitmus BRAJ BHUSHAN SINGH (9 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

Abhishek Singh  (9 years ago)

Fix 1st digit as 1, then remaining two digits can be [9, 8] and [8, 9] ---- total 2
Fix 1st digit as 2, then remaining two digits can be [9,7], [8,8], [7,9] and --- total 3
Fix 1st digit as 3, the remaining two digits can be [9,6], [8,7], [7,8], [6,9]--- total 4
Fix 1st digit as 4, the remaining two digits can be [9,5], [8,6], [7,7], [5,9], [6,8] --- total 5

and so on... till 1st digit is fixed as 9 whose total is 10
So adding all we get:
2 + 3 + 4+ .....+ 10 =[ (10*11)/2 ] -1 = 55 -1 = 54

Is this solution Helpfull? Yes (14) | No   

Ashish  (9 years ago)

I think its 54

990 - 2 combinations
981-6 combinations
972-6 combinations
963-6 combinations
954-6 combinations
882-3 combinations
873-6 combinations
864-6 combinations
855 -3 combinations
774- 3 combinations
765 -6 combinations
666-1 combination

Is this solution Helpfull? Yes (7) | No   

spandita  (9 years ago)

sum is 18 implies no.divisible by 9, so find no. of 3 digit no. ivisible b 9. ans-89

Is this solution Helpfull? Yes (1) | No (3)  

subhasish ghosh  (9 years ago)

1+8+9=3! comination
in this way 2+7+9
2+8+8
3+6+9
3+7+8
4+5+9
4+6+8
4+7+7
5+5+8
5+6+7
total 60 comnination number and 6+6+6 it has only 1 combination .
60+1=61 (ans)

Is this solution Helpfull? Yes (1) | No (2)  

Shobhit Maurya  (9 years ago)

Fix last digit maximum and then 1 to 5 as a first digit, fill the middle number
1 9--->8==189(ways)--->3!
2 9--->7(ways)--->3!
3 9--->6(ways)--->3!
4 9--->5(ways)--->3!
5 9--->4 (ways)--->3!
2nd set (no starting with 1 will be eliminated since 1 cannot be summed to become 18 with other no)
1 8--->NOT POSSIBLE
2 8--->8(ways)--->3!
3 8--->7(ways)--->3!
4 8--->6(ways)--->3!
5 8--->5 (ways)--->3!
KEEP an eye on the previous results while writing the results of combinations
3rd set
4 7-->7(ways)--->3!
5 7--->6 (ways)--->3!
4TH set
From here on number will be repetitive
66 is the ANSWER

Is this solution Helpfull? Yes (1) | No   

sonu kumar  (9 years ago)

1+8+9=3! comination
in this way 2+7+9=6 comb.
2+8+8= 3 comb.
3+6+9= 6
3+7+8 = 6
4+5+9=6
4+6+8=6
4+7+7= 3 comb
5+5+8= 3 comb
5+6+7= 6
6+6+6 = 1 combination
TOTAL = 52 COMBINATIONS.
60+1=61 (ans)

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pavan  (9 years ago)

990/18=55
55-1=54....

Is this solution Helpfull? Yes | No (1)  

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